Ultrametric Distance in Syntax
Abstract
Phrase structure trees have a hierarchical structure.
In many subjects, most notably in {\bf taxonomy} such tree structures
have been studied using ultrametrics.
Here syntactical hierarchical phrase trees are subject
to a similar analysis, which is much simpler as the branching structure is
more readily discernible and switched. The occurrence of hierarchical
structure elsewhere in linguistics is mentioned.
The phrase tree can be represented
by a matrix and the elements of the matrix can be represented by triangles.
The height at which branching occurs is not prescribed in previous syntactic
models, but it is by using the ultrametric matrix.
In other words the ultrametric approach gives a complete description of
phrase trees, unlike previous approaches.
The ambiguity of which branching height to choose,
is resolved by postulating that branching occurs
at the lowest height available.
An ultrametric produces a measure of the
complexity of sentences: presumably the complexity of sentences increases
as a language is acquired so that this can be tested.
All ultrametric triangles are equilateral or isosceles.
Here it is shown that \={X}
structure implies that there are no equilateral triangles.
Restricting attention to simple syntax a minimum ultrametric distance between lexical
categories is calculated.
A matrix constructed from this ultrametric distance
is shown to be different than the matrix obtained from features.
It is shown that the definition of {\sc c-command}
can be replaced by an equivalent ultrametric definition.
The new definition invokes a minimum distance between nodes and
this is more aesthetically satisfying than previous varieties of definitions.
From the new definition of {\sc c-command} follows a new definition of
of the central notion in syntax namely {\sc government}.
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Archival date: 2015-11-21
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Added to PP index
2014-02-26
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2014-02-26
Total downloads
207 ( #12,449 of 37,098 )
Recent downloads (6 months)
19 ( #17,549 of 37,098 )
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